how do you solve polynomial equations by factoring when there is a number without a variable at the end such as: y^2+ 12y+ 27= 0 ?

Question

amistre64 · Answer

have you tried subtracting it to the other side?

amistre64 · Answer

the trick is to add 0

amistre64 · Answer

but a 0 that is useful

amistre64 · Answer

see that number next to the "y" ... the 12?  halve it and square the results

amistre64 · Answer

y^2+ 12y+ 27= 0  ; 12/2 = 6,  6^2 = 36

y^2 +12y +36 -36 +27 = 0

(y^2 +12y +36) -36 +27 = 0

(y+6)^2 -9 = 0

anonymous · Answer

well, this is as far as ive gotten: y (y+12) + 27 = 0
i was told to factor out and the only thing i saw was the "Y" but the 27 didnt have a "Y" so i just left it out.

amistre64 · Answer

you did fine, but that way doesnt really get us to something useful; so we have to use other tricks that math provides

diyadiya · Answer

isn't it  (y+3)(y+9) ??

anonymous · Answer

i think what we're trying to find is what numbers could "Y" be to cause the equation to equal 0.

anonymous · Answer

it may be but im not sure how to get there. :/

amistre64 · Answer

(y+6)^2 -9 = 0

(y+6)^2 = 9   ; now we sqrt both sides

y+6 = +- sqrt(9)

y+6 = +- 3

y = -6 -3  , or y = -6 + 3

amistre64 · Answer

your trying to think linearly; but this isnt a line equation; its a curve, a parabola to be exact

diyadiya · Answer

:D

amistre64 · Answer

try to read up on a method called "completeing the square"